Search Results (8)

We study single-machine group green scheduling considering group setup time deterioration effects and job-processing time learning effects, where the setup time of a group is a general deterioration function on its starting setup time and the processing time of a job is a non-increasing function on its position. We focus on confirming the job schedule for each group and group schedule for minimizing the total weighted completion time. It is proved that this problem is NP-hard. According to the problem’s NP-hardness, we present some optimal properties (including lower and upper bounds) and then propose a branch-and-bound algorithm and two heuristic algorithms (including the modified Nawaz–Enscore–Ham algorithm and simulated annealing algorithm). Finally, numerical simulations are provided to indicate the effectiveness of these algorithms, which demonstrates that the branch-and-bound algorithm can solve random instances of 100 jobs and 14 groups within reasonable time and that simulated annealing is more accurate than the modified Nawaz–Enscore–Ham algorithm. Full article

This work studies single-machine scheduling with general position-dependent deterioration, where job processing times are general non-decreasing functions dependent on their positions in a sequence. The goal is to find a job sequence such that makespan is minimized. The problem can be extended to deal with green scheduling environment where processing time increases due to additional carbon-reduction procedure. Under some optimal properties, we prove that the problem is solved by the largest processing time (denoted by LPT) first rule. Full article

In response to the challenges of dynamic adaptability, real-time interactivity, and dynamic optimization posed by the application of existing deep reinforcement learning algorithms in solving complex scheduling problems, this study proposes a novel approach using graph neural networks and deep reinforcement learning to complete the task of job shop scheduling. A distributed multi-agent scheduling architecture (DMASA) is constructed to maximize global rewards, modeling the intelligent manufacturing job shop scheduling problem as a sequential decision problem represented by graphs and using a Graph Embedding–Heterogeneous Graph Neural Network (GE-HetGNN) to encode state nodes and map them to the optimal scheduling strategy, including machine matching and process selection strategies. Finally, an actor–critic architecture-based multi-agent proximal policy optimization algorithm is employed to train the network and optimize the decision-making process. Experimental results demonstrate that the proposed framework exhibits generalizability, outperforms commonly used scheduling rules and RL-based scheduling methods on benchmarks, shows better stability than single-agent scheduling architectures, and breaks through the instance-size constraint, making it suitable for large-scale problems. We verified the feasibility of our proposed method in a specific experimental environment. The experimental results demonstrate that our research can achieve formal modeling and mapping with specific physical processing workshops, which aligns more closely with real-world green scheduling issues and makes it easier for subsequent researchers to integrate algorithms with actual environments. Full article

Green scheduling that aims to enhance efficiency by optimizing resource allocation and job sequencing concurrently has gained growing academic attention. To tackle such problems with the consideration of scheduling and resource allocation, this paper considers a single-machine group scheduling problem with common/slack due-date assignment and a controllable processing time. The objective is to decide the optimized schedule of the group/job sequence, resource allocation, and due-date assignment. To solve the generalized case, this paper proves several optimal properties and presents a branch-and-bound algorithm and heuristic algorithms. Numerical experiments show that the branch-and-bound algorithm is efficient and the heuristic algorithm developed based on the analytical properties outruns the tabu search. Full article

From the perspective of energy efficiency and environmental sustainability, the scheduling problem in a flexible workshop with the utilization of automated guided vehicles (AGVs) was investigated for material transportation. Addressing the dual-constrained integrated scheduling challenge involving machining machines and AGVs, a scheduling optimization model was established with makespan, workshop energy consumption, and processing quality as the optimization objectives. To effectively solve this model, an enhanced whale optimization algorithm (IWOA) was proposed. Specifically, nonlinear convergence factors, adaptive inertia weights, and improved helix positions were introduced into the standard whale optimization algorithm to update the model. Furthermore, a loss function was constructed based on fuzzy membership theory to obtain the optimal compromise solution of the multi-objective model. The research results indicate that: (1) The IWOA obtained the optimal solutions on benchmark instances MK01, MK02, MK04, MK07, and MK08; (2) The IWOA outperformed the WOA(1), WOA(2), WOA-LEDE, and NSGA-II algorithms in the two instances provided in this paper, demonstrating strong robustness of the model; (3) Although the multi-objective model constructed in this paper could not surpass the single-objective optimal solution in individual objectives, it achieved compensation in other objectives, effectively balancing the trade-offs among the makespan, workshop energy consumption, and processing quality of the three objectives. This research offers an effective practical approach to address green flexible workshop scheduling with AGV transportation. Full article

In this paper, we study a single-machine green scheduling problem with learning effects and past-sequence-dependent delivery times. The problem can be properly applied to tackle green manufacturing where production and delivery time are variable and highly subject to process-reengineering. Our goal is to determine the optimal sequence such that total weighted completion time and maximum tardiness are minimized. For the general case, we provide the analysis procedure of lower bound, and also propose the heuristic and branch-and-bound algorithms. Furthermore, computational experiments are conducted to demonstrate the effectiveness of our algorithms. Full article

Green manufacturing, which takes environmental effect and production benefit into consideration, has attracted increasing concern with the target of carbon peaking and carbon neutrality proposed. As a critical process in the manufacturing system, shop scheduling is also an important method for enterprises to achieve green manufacturing. Therefore, it is necessary to consider both production benefits and environmental objectives in shop scheduling, which are symmetrical and equally important. In addition, noise pollution has become an important environmental issue that cannot be ignored in the manufacturing processes, but which has been paid less attention in previous studies. Thus, the MODABC algorithm, with the optimization objectives of simultaneously minimizing lead-time/tardiness cost and job-shop noise pollution emission is proposed in this paper. We designed a discrete permutation-based two-layer encoding mechanism to generate the initial population. Then, three crossover methods were used to perform nectar update operations in the employed bee search phase, and three neighbourhood structures were used to improve the onlooker bee search operations. Finally, the MODABC algorithm was compared with other classical MOEAs. The results demonstrate that MODABC can provide non-dominated solution set with good convergence and distribution, and show significant superiority in solving green single-machine multi-objective scheduling problems. Full article

This research focuses on an Order Acceptance Scheduling (OAS) problem on a single machine under time-of-use (TOU) tariffs and taxed carbon emissions periods with the objective to maximize total profit minus tardiness penalties and environmental costs. Due to the NP-hardness of the considered problem especially in presence of sequence-dependent setup-times, two fix-and-relax (FR) heuristics based on different time-indexed (TI) formulations are proposed. A metaheuristic based on the Dynamic Island Model (DIM) framework is also employed to tackle this optimization problem. These approached methods show promising results both in terms of solution quality and solving time compared to state-of-the-art exact solving approaches. Full article